Analysis of two-color laser-induced electron emission from a biased metal surface using an exact quantum mechanical solution

Abstract

Photoelectron emission from solids driven by high intensity lasers offers a platform for the coherent control of electron motion in ultrashort spatiotemporal scales. By solving the time-dependent Schrödinger equation, we present an exact analytical solution for the nonlinear ultrafast electron emission from a dc biased metal surface illuminated by two-color laser fields. We systematically examine the combined effects of a dc electric field and the two-color laser fields. In addition to the remarkable tunability of electron emission processes due to the interference of the two-color laser fields, we find that a strong dc electric field not only opens up more tunneling emission channels, but also introduces intense modulation to the emission current. We found the surprising results that strong current modulation (with respect to the phase difference of the two-color lasers) persists (>70%) even with a large dc bias (i.e. ratio of the electric fields for dc : fundamental laser : second harmonic laser 1 : 0.5 : 0.07). In the meantime, the average emission current level increases by about three orders of magnitude compared to the case of zero dc bias. Application of our model to time-resolved photoelectron spectroscopy is exemplified, showing the dynamics of the n-photon excited states depends strongly on the applied dc field. Our study suggests a practical way to maintain a strong modulation to high current photoemission, by the addition of a large dc bias for two-color laser induced electron emission.

Plasmon-Enhanced Resonant Photoemission Using Atomically Thick Dielectric Coatings

“…Here, ϵ is the longitudinal energy of electrons inside the metal impinging on the metal surface. To calculate the photoemission current, we employ a quantum theory of photoemission (see Methods), ,,, which is the exact solution of the time-dependent Schrödinger equation subject to an oscillating triangular barrier. Therefore, we first need to approximate the irregular “double-barrier” potential profiles with an effective triangular barrier, as exemplified in Figure a.…”

“…A quantum mechanical model ,,, is used to calculate the photoelectron emission current density from both bare and coated metal surfaces driven by laser fields. The model is assumed to be one-dimensional, in which electrons impinge normally to the metal surface.…”

“…Based on this oscillating triangular barrier, exact analytical solutions are obtained ,,, for the incident electron wave ψ i inside the metal and transmitted electron wave ψ t outside the metal using Truscott transformations from eq , which read: where ϵ is the electron initial energy, and are the electron wave numbers, T j (or R j ) is the electron wave transmission (or reflection) coefficient, E j = ϵ + j ℏω – W eff – E F – U P with ponderomotive energy U P = e 2 F eff 2 /4 mω 2 , the parameter ξ = z + eF eff cos­(ω t )/ m ω 2 , and the integer j indicates the j -photon process.…”

“…Photoelectron emission, or photoemission, from a nanotip driven by an ultrafast laser offers an attractive route to generate high brightness, low emittance, and spatiotemporally coherent electron bunches, − which are central to time-resolved electron microscopy, free-electron lasers, carrier-envelope-phase detection, and novel nanoelectronic devices. − Despite extensive research exploring efficient multiphoton absorption at low laser intensities or optical field tunneling at high laser intensities, ,− the use of photoemission from nanotips is still limited by its low emission current and low quantum efficiency. It has been proposed to enhance the photoemission by adding a strong dc bias, ,,− but the optical field enhancement near the apex of the nanotip is still relatively low, typically only 10 times, , making the optical field tunneling accessible only at high incident laser fields, e . g ., 1.22 V/nm …”

Quantum interference visibility spectroscopy in two-color photoemission from tungsten needle tips

“…This control scheme was also applied to metallic nanoemitters. Photoemission from the surface of metallic needle tips driven by two-color femtosecond laser fields has shown a remarkably large coherence, indicated by a visibility reaching 97.5% [29][30][31][32][33]. This photoemission displayed a homogeneous modulation for all emitted electron energies, driven with a two-color frequency pair of fundamental and second-harmonic (ω-2ω).…”